Image invariants are properties of images of an object that remain unchanged with changes in parameters of a camera and/or illumination. For example, geometric invariants are related to apparent size of different parts of objects and are therefore equally valid for the objects with any reflectance characteristics of the surface, including diffuse, specular and transparent objects. However, in order to use the geometric invariants from the images of the object, point correspondences across the images should be identified. Identifying the point correspondences from images of the diffuse object is a meaningful task since the diffuse object has photometric features. But specular object, i.e., the object having surface with mirror-like reflectance, does not have an appearance of its own, but rather present a distorted view of an environment surrounding the object.
Therefore, identifying the point correspondences using an image feature descriptor of the specular object is challenging. The image feature descriptor finds correspondences between reflections of the environment, which do not correspond to the same points on the surface of the object. Thus, there is a need to find photometric properties of the specular object that are invariant to the surrounding environment.
Points of parabolic curvature are fundamental to perception of a shape of the diffuse and/or the specular objects. Because these points correspond to a geometric property of the surface, these points can then be used for a variety of machine vision tasks such as object recognition, pose estimation and shape regularization.
Accordingly, it is desired to determine photometric properties of the images of mirror surfaces around points that exhibit parabolic curvature without knowledge about shape of the surface of the specular object and/or the surrounding environment.